You know, with the word "heaven" in their name, one would automatically assume that they were a religious group therefore spiritual. But... they were into aliens. The only way I can rationally harmonize this is that they were ancient alien theorists.
No, they were a New Age UFO cult lead by an obviously schizophrenic person (Marshall Applewhite). His story is actually rather sad. He was a self-hating gay man and ended up castrating himself. He needed serious help and never got it. He wasn't an evil person, from what I can tell. He wasn't Jim Jones. He really went into the deep end after the woman he started the cult with and who was his best friend and life partner died. Then he broke from reality, becoming obsessed with the apocalypse (which was a 180 for him), increasingly paranoid, etc.
They did have spiritual teachings, like belief in a soul and afterlife, but they made zero sense. Somehow their souls were to be picked up in a spaceship, and his dead friend's soul was also on board, and they would all go and live happily on another planet. It was obviously just an excuse to kill themselves as he didn't want to live anymore, and was obviously very upset over his friend dying. I think he just wanted to be with her, really. I have no clue how or why any of his followers believed it.